Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-2y &= -9 \\ 2x+2y &= 9\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = -2x+9$ Divide both sides by $2$ to isolate $y$ $y = {-x + \dfrac{9}{2}}$ Substitute this expression for $y$ in the first equation. $-x-2({-x + \dfrac{9}{2}}) = -9$ $-x + 2x - 9 = -9$ Simplify by combining terms, then solve for $x$ $1x - 9 = -9$ $1x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $- 0-2y = -9$ $-2y = -9$ $-2y = -9$ $y = \dfrac{9}{2}$ The solution is $\enspace x = 0, \enspace y = \dfrac{9}{2}$.